Segregation Enthalpy Research Articles

Grain boundary segregation for the Fe-P system: Insights from atomistic modeling and Bayesian inference

In this work we re-assess experimental data for grain boundary (GB) segregation of P in bcc Fe with thermodynamic and statistical methods. The data are based on Auger-Electron-Spectroscopy (AES) measurements which have provided P GB concentrations for various bulk contents and temperatures for ferrite. While in the previous investigations of this system a single-site McLean equation was used to extract segregation enthalpy and entropy, we employ multi-site segregation models as suggested by atomistic simulations. We use a recently introduced methodology based on inter-atomic potentials to calculate the segregation energy spectrum, as well as vibrational entropy and solute-solute interactions of P in polycrystalline Fe, thereby obtaining a three-dimensional distribution of energy, entropy and interactions. Using this trivariate distribution we predict P GB concentrations and compare them to the experimental measurements. Furthermore, we calibrate the parameters of physical models of increasing complexity to the experimental data with an inverse modeling approach based on Bayesian inference. While it is not possible to seamlessly link the results from AES to atomistic modeling, our investigation provides significant new insights for thermodynamic modeling of GB segregation. The vibrational entropy deduced from experiment differs from physics based atomistic simulations even when taking the spectral nature of energy, entropy and interactions into account. However, the correlations of the quantities are in good agreement when considering the trivariate model. Our investigation highlights the need for new and more accurate experimental datasets of GB segregation.

In situ study and assessment of the phosphorus-induced solute drag effect on the grain boundary mobility of austenite

The solute drag effect of phosphorus (P) in the single-phase austenite (γ-Fe) region was studied under isothermal annealing conditions at temperatures of 1050 °C, 1150 °C, 1250 °C and 1350 °C. High-temperature laser scanning confocal microscopy (HT-LSCM) was used to observe and quantify in situ grain growth on the surface of three different samples containing 0.026 wt.-% P, 0.044 wt.-% P and 0.102 wt.-% P. The dependence of the arithmetic mean grain sizes on time and temperature were modeled mathematically using a simple ordinary differential equation (ODE) according to normal grain growth (NGG) theory. As no other major effects, i.e., Zener-pinning by precipitates, occurred under the selected experimental conditions, grain growth interference was only considered by grain boundary (GB) segregation of P. Thus, the total grain boundary mobility (M) was directly determined depending on the P content and isothermal annealing temperature. The fitted GB mobility values enabled the determination of an average binding energy value between impurity P atoms and grain boundaries (E0 = -1.1 - -0.6 eV) in the system. Finally, the GB segregation of P in γ-Fe was derived from the observed grain growth kinetics. The results showed reasonable agreement with calculations using segregation enthalpies from the literature.

Revealing the deformation mechanisms of 〈110〉 symmetric tilt grain boundaries in CoCrNi medium-entropy alloy

The synergy of multiple deformation mechanisms responsible for the excellent mechanical properties attracts an increasing interest in CoCrNi medium entropy alloy (MEA). In this study, we employed molecular dynamics simulations to investigate the chemical properties of grain boundaries (GBs) and their influence on deformation mechanisms in CrCoNi MEA, with particular emphasis on role of lattice distortion and short-range order (SRO) in dislocation plasticity. After aging, we found Ni element segregate at GB through short-range diffusion driven by a more negative segregation enthalpy. The degree of SRO within the GB region is significantly correlated with the Ni concentration, and it markedly influences the structure and local stress distribution of the GB. Compared to the lattice distortion, SRO can effectively suppress the GB dislocations nucleation and slip, thereby increasing yield strength of the material. During the plastic stage, although the deformation microstructure is intimately linked to the active slip systems and grain orientation, the presence of SRO, as well as the resultant rugged dislocation pathways and increased slip resistance lowers the propensity for stacking faults and phase transformation. The current findings can enhance a fundamental comprehension of diverse deformation mechanisms in CoCrNi MEA and suggest that the chemical characteristics of GB could serve as a pivotal approach for modifying the mechanical properties of MEAs.

Grain size stabilization in pure, Co, Mg and Al-doped nickel oxide

Grain size stabilization is essential for employing nickel oxide (NiO) for energy-related applications. Hence, it is investigated in NiO by adding Co, Mg and Al as solutes. Pure and doped NiO with 2–5 mol% Co, Mg, and Al are synthesized at 720, 920 °C. The composition distribution maps from energy dispersive spectroscopy reveal that Al-concentration is the highest at NiO grain boundaries. This is supported by its highest calculated segregation enthalpy (ΔHseg). This leads to ∼82% reduction in grain size in Al-doped NiO (∼24 nm, 5%Al, 720 °C) vis-à-vis ∼33% and ∼0.6% in Mg-doped and Co-doped NiO, respectively. Isothermal annealing of pure and 5% doped NiO at 620–920 °C for up to 300 min is conducted to study the grain size stability. Al-doped NiO yields ∼14 nm followed by Mg, Co-doped and pure NiO at ∼41, ∼53 and ∼55 nm, respectively at 620 °C. The estimated activation energy (Q) for grain growth is ∼504 kJ mol−1 in Al-doped NiO. Those in pure, CO, Mg-doped NiO are within ∼121–138 kJ mol−1. The highest Q in Al-doped NiO results in its lowest stabilized grain size during isothermal annealing. This work is useful in selecting a suitable solute and its concentration for grain size stabilization.

Oscillatory Mechanism of α-Fe(N) ↔ γ'-Fe4N Phase Transformations during Nanocrystalline Iron Nitriding.

The kinetics of nanocrystalline α-iron nitriding to γ’-iron nitride in an ammonia atmosphere was studied at 598–648 K and at atmospheric pressure. Oscillatory changes in nitriding reaction rates depending on nitrogen concentration in a solid sample were observed. This phenomenon was explained by a gradual change in the iron active surface coverage degree, with nitrogen resulting from a gradual change in the free enthalpy of nitrogen segregation. The α-Fe(N) nanocrystallites’ transformation into γ’-Fe4N went through six metastable FeNx states. The continuous function proposed by Fowler and Guggenheim was modified to a stepwise variable function.

Rationalization of the sub-surface segregation in nanoalloys of weakly miscible metals.

The origin of the stability of sub-surface precipitates in core-shell bimetallic nanoparticles is investigated from the perspective of atomic-size effects for systems where the core atoms have a size equal to, or lower than, the shell atoms. With the aim of providing more general assessments, a systematic study is proposed by considering three model systems combining weakly miscible metals: IrPd (negligible lattice mismatch, Δr/rPd = -1%), AuRh (moderate lattice mismatch, Δr/rAu = -7%) and AuCo (large lattice mismatch, Δr/rAu = -13%). The main driving forces for sub-surface segregation and the characteristic core morphologies are quantified from the combination of Monte Carlo and quenched molecular dynamics simulations. The preferential occupation of the sub-surface shell by an impurity of Ir or (Co or Rh) in a Pd or Au nanoparticle, respectively, in particular at the sub-vertex sites, is found to be a common feature in these dilute nanosystems. With the help of a model of the decomposition of the segregation enthalpies, it is shown that the dominant driving forces leading to the preferential sub-surface segregation at the vertex sites can be very different from one system to another: atomic size (AuCo, large lattice mismatch), coupled alloy-size-cohesion (AuRh, moderate lattice mismatch) or coupled alloy-cohesion (IrPd, negligible lattice mismatch) effects. As a consequence, in the core-shell nanoalloys, in the first stage of enrichment of an Au nanoparticle with Co or Rh core atoms, or a Pd nanoparticle with Ir core atoms, all the equilibrium structures consist of similar off-center solute clusters anchored at sub-vertex sites, and this is regardless of the lattice mismatch.

Impact of the segregation energy spectrum on the enthalpy and entropy of segregation

Substantial disagreement exists for segregation energies between experimentally measured and first principles calculated values. To resolve this standing issue, we computed segregation of five different elements to the same grain boundaries as studied in an previous experimental investigation. We show that the multi-site nature of segregation leads to a strong artificial temperature dependence in the single site effective segregation energy. Taking this into account leads to a highly improved agreement between experiment and theory and clarifies the nature of experimentally determined segregation enthalpies and entropies.

Improved Al-Mg alloy surface segregation predictions with a machine learning atomistic potential

Various industrial/commercial applications use Al-Mg alloys, yet the Mg added to Al materials, to improve strength, is susceptible to surface segregation and oxidation, leaving behind a softer and Al-enriched bulk alloy. To better understand this process and provide a systematic methodology for investigating dopants that can mitigate corrosion, we have developed a robust atomistic deep neural net potential (DNP) using a dataset generated with first-principles density-functional theory (DFT). The potential, validated systematically against DFT values, has been shown to have a high fidelity in calculating different elemental and intermetallic Al-Mg systems' properties. Our calculations predict a linear trend in the formation energy of the Al-Mg alloy and its density as a function of temperature, consistent with experimental literature. Employing the DNP within a hybrid Monte Carlo and molecular dynamics (MC/MD) approach, we predict anisotropic surface segregation for Al-Mg alloys such that (111)(100)(110), with (111) surfaces displaying the lowest segregation enthalpies and Mg enrichment. Furthermore, we model the segregation tendencies by adapting a recently introduced isotherm model for grain boundary segregation. Our results show that this model describes the MC/MD segregation profiles with higher fidelity than the McLean and Fowler-Guggenheim isotherm models.

Entropy matters in grain boundary segregation

Starting with a fairly comprehensive database on experimental results on enthalpy and entropy of grain boundary segregation, the detrimental influence of ignoring the segregation entropy term is shown for the latter as well as for additional examples of intergranular cohesion, the stability of nanograin size, and the segregation enthalpy-segregation entropy compensation effect. Furthermore, the decisive role of segregation entropy in the transition from substitutional to interstitial segregation with increasing temperature, and the newly explored effect of entropy-dominated grain boundary segregation are presented. Despite the direct evidence of the importance of entropy in grain boundary segregation, its contribution has been frequently neglected in the literature. One of the possible reasons is that the routines for a theoretical determination of the segregation entropy are still missing. We hope that, in the near future, progress in advanced theoretical methods will substantially improve our present understanding of grain boundary segregation.

Learning grain boundary segregation energy spectra in polycrystals

The segregation of solute atoms at grain boundaries (GBs) can profoundly impact the structural properties of metallic alloys, and induce effects that range from strengthening to embrittlement. And, though known to be anisotropic, there is a limited understanding of the variation of solute segregation tendencies across the full, multidimensional GB space, which is critically important in polycrystals where much of that space is represented. Here we develop a machine learning framework that can accurately predict the segregation tendency—quantified by the segregation enthalpy spectrum—of solute atoms at GB sites in polycrystals, based solely on the undecorated (pre-segregation) local atomic environment of such sites. We proceed to use the learning framework to scan across the alloy space, and build an extensive database of segregation energy spectra for more than 250 metal-based binary alloys. The resulting machine learning models and segregation database are key to unlocking the full potential of GB segregation as an alloy design tool, and enable the design of microstructures that maximize the useful impacts of segregation.

The influence of alloying in stabilizing a faceted grain boundary structure

Grain boundary structures have long been known to depend on factors such as solutes and temperature. In this work, in-situ atomic scale imaging was used to observe the faceting of a Σ21a [1 1 1]-tilt-axis boundary at 600 ∘C and 800 ∘C in a Pt-5Au (at. %) nanocrystalline alloy. With an increase in temperature, we observe an evolution from many, shorter facets to fewer, longer facets. The preferred facets are shown to be symmetrically equivalent tilt boundaries, via the fundamental zone formalism. Simulation of Pt bicrystals reveals that these preferred facets do not lie in an energy minimum (of the tilt boundaries that the grain boundary misorientation could access); however, calculation of the segregation enthalpy of Au to these grain boundary lattice sites indicates a greater preference of Au, reducing the grain boundary energy, and explaining the facet stabilization observed.

Quantitative prediction of Suzuki segregation at stacking faults of the γ’ phase in Ni-base superalloys

Recent experiments suggest that Suzuki segregation may play an important role during deformation in Ni-base superalloys at intermediate temperatures. In this study, a segregation isotherm model incorporating segregation enthalpy from ab initio calculations is proposed to predict quantitatively solute enrichment at superlattice intrinsic stacking faults (SISF) within the γ’ precipitates in Ni-base superalloys. A sublattice model is employed to describe the γ’ phase. A strong correlation between segregation enthalpy and solute enrichment is found. Even though the segregation enthalpy is relatively small, the predicted solute enrichment is consistent with experimental observations. The simulation predictions also suggest a strong cross-correlation among different alloying elements. For example, it is found that segregation of Co on the Ni sublattice at the fault draws segregation of Cr that has a positive segregation enthalpy at the fault without the presence of Co. Such quantitative predictions of equilibrium segregation of solutes at stacking faults in γ’ precipitates and its effect on the stacking fault energy could aid the investigation of deformation mechanisms and help the design of superalloys.

Intrinsic and extrinsic conduction contributions at nominally neutral domain walls in hexagonal manganites

Conductive and electrostatic atomic force microscopy (cAFM and EFM) are used to investigate the electric conduction at nominally neutral domain walls in hexagonal manganites. The EFM measurements reveal a propensity of mobile charge carriers to accumulate at the nominally neutral domain walls in ErMnO3, which is corroborated by cAFM scans showing locally enhanced direct current conductance. Our findings are explained based on the established segregation enthalpy profiles for oxygen vacancies and interstitials, providing a microscopic model for previous, seemingly disconnected observations ranging from insulating to conducting behavior. In addition, we observe variations in conductance between different nominally neutral walls that we attribute to deviations from the ideal charge-neutral structure within the bulk, leading to a superposition of extrinsic and intrinsic contributions. Our study clarifies the complex transport properties at nominally neutral domain walls in hexagonal manganites and establishes the possibility to tune their electronic response based on oxidation conditions, opening the door for domain-wall-based sensor technology.

Temporally resolved LEIS measurements of Cr segregation after preferential sputtering of WCrY alloy

The dynamic behaviour of thermally driven segregation of Cr to the surface of WCrY smart alloy is studied with low energy ion scattering (LEIS). Sputtering the WCrY sample with 500 eV D2+ ions at room temperature results in preferential removal of the lighter alloy constituents and causes an almost pure W surface layer. At elevated temperatures above 700 K the segregation of Cr atoms towards the surface sets in and prevents the formation of a pure W layer. The simultaneous heating and sputtering of the sample leads to a surface state which reflects the balance between sputter removal and segregation flux, and deviates from the equilibrium due to thermally driven segregation. Stopping the sputter ion beam allows the system to relax and develop toward the segregation equilibrium. The time constants for the temporal changes of W and Cr surface coverage are obtained from a series of LEIS measurements. The segregation enthalpy is determined from the time constants obtained for various sample temperatures.

Few-monolayer yttria-doped zirconia films: Segregation and phase stabilization.

For most applications, zirconia (ZrO2) is doped with yttria. Doping leads to the stabilization of the tetragonal or cubic phase and increased oxygen ion conductivity. Most previous surface studies of yttria-doped zirconia were plagued by impurities, however. We have studied doping of pure, 5-monolayer ZrO2 films on Rh(111) by x-ray photoelectron spectroscopy (XPS), scanning tunneling microscopy (STM), and low-energy electron diffraction (LEED). STM and LEED show that the tetragonal phase is stabilized by unexpectedly low dopant concentrations, 0.5 mol % Y2O3, even when the films are essentially fully oxidized (as evidenced by XPS core level shifts). XPS also shows Y segregation to the surface with an estimated segregation enthalpy of -23 ± 4 kJ/mol.

Segregation and preferential sputtering of Cr in WCrY smart alloy

The temperature driven segregation of Cr to the surface of the tungsten-based WCrY alloy is analysed with low energy ion scattering of He+ ions with an energy of 1 keV in the temperature range from room temperature to 1000 K. Due to the high surface sensitivity, these measurements probe only the composition of the outermost monolayer. The surface concentration of Cr increases slightly when the temperature of the sample is increased up to 700 K and exhibits a much stronger increase when the sample temperature is further raised. The segregation enthalpy for Cr is obtained from the Langmuir-McLean relation and amounts to 0.7 eV. The surface concentration of Y shows a similar behaviour to the Cr concentration. The temperature thresholds between slow and accelerated surface density increases for Cr and Y are nearly the same. At a temperature of 1000 K the low energy ion scattering detects almost no W on the surface. The modified surface composition due to the segregated species, i.e. the mixed Cr/Y layer, stays stable during cool-down of the sample. Preferential sputtering is investigated using ion bombardment of 250 eV D atoms, resulting in an increase of the W surface density at room temperature. This effect is counteracted at elevated temperatures where segregation replenishes the lighter elements on the surface and prevents the formation of an all-W surface layer. The flux of segregating Cr atoms towards the surface is evaluated from the equilibrium between sputter erosion and segregation.

A strategy for designing stable nanocrystalline alloys by thermo-kinetic synergy

Aiming to design stable nanocrystalline (NC) materials, so far, it has been proposed to construct nanostructure stability maps in terms of thermodynamic parameters, while kinetic stabilization has seldom been considered, despite the synergy of thermodynamics and kinetics. Consequently, the thermodynamically stabilized NC materials may be easily subjected to grain growth at high temperatures due to the weakly kinetic stabilization. Starting from the thermo-kinetic synergy, a stabilization criterion is proposed as a function of intrinsic solute parameters (e.g. the activation energy for bulk diffusion and the segregation enthalpy), intrinsic solvent parameters (e.g. the intrinsic activation energy for GB migration and the GB energy) and processing parameters (e.g. the grain size, the temperature and the solute concentration). Using first-principles calculations for a series of combinations between fifty-one substitutional alloying atoms as solute atoms and Fe atom as fixed solvent atom, it is shown that the thermal stability neither simply increases with increasing the segregation enthalpy as expected by thermodynamic stabilization, nor monotonically increases with increasing the activation energy for bulk diffusion as described by kinetic stabilization. By combination of thermodynamic and kinetic contributions, the current stabilization criterion evaluates quantitatively the thermal stability, thus permitting convenient comparisons among NC materials involved by various combinations of the solute atoms, the solvent atoms, or the processing conditions. Validity of this thermo-kinetic stabilization criterion has been tested by current experiment results of Fe-Y alloy and previously published data of Fe-Ni, Fe-Cr, Fe-Zr and Fe-Ag alloys, etc., which opens a new window for designing NC materials with sufficiently high thermal stability and sufficiently small grain size.

Li2O‐doped MgAl2O4 nanopowders: Energetics of interface segregation

AbstractManufacturing nanoceramics is challenging owing to the instability of the grain size resulting from the high driving force toward growth associated with the interfaces. Nanometric ceramics of some oxides have exceptional mechanical and optical properties, eg, magnesium aluminate spinel (MgAl2O4). The production of these fully conformed ceramics requires a precursor powder, which generally contains sintering‐promoting additives. Li salts are typically used as sintering promoters for MgAl2O4, but the interface stability associated with the segregation of the additive is poorly understood. In this study, MgAl2O4 samples containing 0‐2.86 mol% Li ions were synthesized via a simultaneous‐precipitation method in an ethylic medium and subsequently calcined at 800°C in air. The nanopowders exhibited only the MgAl2O4 phase, and the crystallite size was determined by the Li2O concentration. The crystallite size was changed via the chemical modification of the interfaces by the segregation of Li ions. The solubility in the bulk material was very low at the fabrication temperature, and small amounts of Li ions saturated the bulk material and segregated to the grain boundaries (GBs), significantly stabilizing the grain–grain interface compared with the surface. The resulting powder was then aggregated further owing to the initial stage of sintering. The surface excess obtained via the selective lixiviation method confirmed that the segregation to the GBs was greater than that to the surface. Energetics calculations confirmed these results, indicating a high enthalpy of segregation at the GBs () compared with that at the surfaces (). The enthalpy of segregation together with the interface excess allowed us to estimate the reduction in the interface energy with Li+ segregation of 0.8% to the surface and 11.2% to the GBs. The Li+ segregation to the surfaces started by Al3+ substitution, and for powders with ≥1.8 mol% Li ions, Mg+2 was preferentially substituted at the surfaces.

Grain-boundary segregation of boron in high-strength steel studied by nano-SIMS and atom probe tomography

High resolution imaging by secondary ion mass spectrometry and atom probe tomography have been employed to investigate boron segregation at austenite grain boundaries (γGBs) after soaking in a high-strength low-carbon steel. The combined use of these two analytical techniques is shown to be powerful for quantifying solute and segregated boron levels. Quenching was performed after soaking aiming to clarify the temperature effect on boron distribution under thermal equilibrium. Boron depletion in the γGBs vicinity was observed in the as-quenched states from high temperatures, suggesting that the cooling rate was not fast enough to limit boron diffusion during cooling. We found that boron segregation at γGBs increases with temperature. This is due to the increase of solute boron concentration in the grains, resulting from boride precipitate dissolution. It appears that the segregation magnitude still follows the equilibrium laws as a function of temperature. From our investigations, it was possible to determine the boron equilibrium segregation enthalpy. These results have important practical consequences for controlling the levels of segregated boron in steels.

Grain boundary diffusion of 59Fe in high-purity copper

Grain boundary diffusion of iron in high purity polycrystalline copper is measured using the radiotracer technique and applying the 59Fe isotope. At lower temperatures, T<949 K, the measurements are performed under Harrison's C-type kinetic regime and the grain boundary diffusion coefficient of Fe in Cu, Dgb, is determined, Dgb=5.6⋅10−6×exp(−121kJmol−1/RT) m2/s. Unconventional penetration profiles are measured for Fe grain boundary diffusion in Cu at higher temperatures (≥ 949 K) under the intended B-type kinetic regime, in fact formal C-type profiles are systematically observed instead. Molecular dynamics simulation with the literature Finnis-Sinclair type interatomic potentials [Ackland et al., Phil. Mag. A, 1997] discovered an unexpected response of Cu grain boundaries on a partial Fe coverage at temperatures above 900 K. A model of Fe penetration in polycrystalline Cu in such conditions is proposed, which explains the untypical shape of the penetration profiles. The combination of the B- and C-type grain boundary diffusion measurements predict a strong segregation of Fe in Cu with a low segregation enthalpy.